Chinese police have lifted Ai Weiwei's strict bail conditions but warned that he cannot leave the country because he is under investigation for pornography, bigamy and other alleged offences, the artist said.

The 54-year-old says the allegations are intended to intimidate him rather than being the basis for a serious inquiry. Friday is the first anniversary of his release after 81 days of detention.

Officials said Ai was investigated for economic crimes, though police never formally notified his family of his detention, and later he was handed a 15m yuan (£1.5m) tax bill. He was barred from leaving Beijing for a year and from using Twitter or granting interviews, though he has done both of the latter.

In an article for the Guardian, Ai warns that all Chinese citizens remain vulnerable until the rule of law is established. He compares his case to those of the disgraced politician Bo Xilai and the activist Chen Guangcheng, who sought refuge in the US embassy in Beijing.

"You can be a high party member or the lowest fighter for rights or a recognised artist … but we all have one thing in common: none of us have been dealt with through fair play, open trials and open discussion," he writes. "China has not established the rule of law and if there is a power above the law there is no social justice. Everybody can be subjected to harm."

He adds: "Stupidity can win for a moment, but it can never really succeed because the nature of humans is to seek freedom. They can delay that freedom but they can't stop it."

Ai told the Guardian: "I went to the police station today and they lifted the bail conditions but gave me a clear warning, saying I couldn't leave the nation. I asked them what the legal basis was and they said there were still cases under investigation: pornography, exchanging foreign currency and bigamy. I don't think they are really willing to openly talk about those things; it is between me and them, to intimidate me."

The pornography allegation is believed to relate to a photograph showing Ai and four women posing naked; he has said they did not touch each other. When the accusation first surfaced, supporters posted nude pictures of themselves in sympathy.

The allegation of illicitly exchanging foreign currency relates to a project in 2008 when he arranged for foreign architects who visited China to be paid in euros by a Swiss gallery, while he got Chinese currency in return.

Ai said police had declined to comment on how long the cases would last and when he would be allowed to travel abroad again. They had previously told him that his passport would be returned when his bail lapsed. Ai was unable to attend last month's opening of the Serpentine summer pavilion, which he co-designed, owing to the travel ban.

"They want me to be low-key and not talk about politics or criticise the government. They said it would be best for me and my family. It's the first time they have mentioned my family and my child and I feel that is strange. In China, I think that's a threat," he said.

Ai has married once and has a young son by another woman.

On Wednesday police barred Ai from attending court as the company that handles his affairs counter-sued authorities over the tax bill. His friend and legal adviser Liu Xiaoyuan was taken away by police before the hearing.

Supporters say the tax case is retaliation for his activism. State media alleged that the company had "evaded a huge amount of taxes and intentionally destroyed accounting documents".